CLOSURE OF THE GOVERNING EQUATIONS OF DEFECT DYNAMICS AND THE RESULTING THEORY OF THE PLASTIC STATE

The equations of defect dynamics are derived from the single system of relations that specifies the time rate of change of the dislocation densities. The resulting source equations are shown to admit a 12-fold gauge group and the resulting kinematic equations are shown to admit a 15-fold gauge group. The generators of the two gauge groups are determined by the requirements that the Burgers and Frank vectors have their classical representations. This determination results in a unique decomposition of all quantities in terms of sums of internal variables and external geometric variables, and represents the first and second closures of the field equations. The presence of a unique external system of geometric variables permits derivation of the forms of the equations of balance of mass, momentum, moment of momentum and energy. The third closure is obtained through use of the practices of nonequilibrium thermodynamics. This results in a system of equations that determines the dislocation currents in terms of the distortion, the dislocation density and the geometric strain measures. A class of models is exhibited wherein most of the properties of plasticity theories are obtained. © 1979.